Population attributable fraction: comparison of two mathematical procedures to estimate the annual attributable number of deaths

Table 1 Conversion table of notations.

Variable	Allison et al [1]	Mokdad et al [2]	This Paper
No. of deaths attributable	ω	ω	ω
Total no. of deaths in population	M	M	M
Total no. in population	N		N
Fraction of population nonexposed	P(R)	P₀	f₀, 1- Σf_i, 1- Σf_i - f_q
Fraction of population exposed	P(O)	Σ P_i	f, Σf_i
Fraction of population exposed to an exposure category (i)		P_i	f_i
Fraction of population exposed to a neutral category (e.g., underweight)	P(Q)		f_q
Hazard ratio (HR) for an exposure category	h		h
Hazard ratio (HR) for a neutral category (e.g., underweight)	q		q
Probability of death in a year in population	P(D), M/N		p, P(D)
Hazard of death in the nonexposed	λ		λ
Conditional probability of death in a year in nonexposed	P(D\|R), 1 - e^-λ		p₀, P(D\|E₀)
Conditional probability of death in a year in various exposure categories	P(D\|O), 1 - e^-hλ		R_i p₀
Conditional probability of death in a year in a neutral category (e.g., underweight)	P(D\|Q), 1 - e^-qλ		p_q
Relative risk	RR, P(D\|O)/P(D\|R)	RR_i	R_i
Population attributable fraction		PAF	PAF